The charmed-strange meson \(D^*_{s0}(2317)\)  was first observed by BABAR Collaboration in the inclusive
\(D^+_s\pi ^0\)  invariant mass distribution [1]}, [2]}, then confirmed by CLEO [3]}
and Belle Collaboration [4]}, respectively. Usually, the \(D^*_{s0}(2317)\)  meson is suggested
as a P-wave \(\bar{c}s\)  state with spin-parity \(J^P=0^+\) . However, there exit two divergences between
the data and the theoretical predictions:
First, the measured mass for this meson is at least \(150 MeV/c^2\)  lower than
the theoretical calculations from a potential model [5]}, [6]}, lattice QCD [7]} and so on.
For example, the authors [8]} obtained \(M(D^*_{s0}(2317))=(2480\pm 30)MeV\)  by using the standard Borel-transformed QCD sum rule which was higher than the BABAR result by about 160 MeV.
While, Narsion [9]} used the QCD spectral sum rules to get \(M(D^*_{s0}(2317))=(2297\pm 113)\)  MeV and reached the conclusion that \(D_s(2317)\)  is a \(\bar{c}s\)  state. Second, the absolute branching ratio of decay
\(D^*_{s0}(2317)^{\pm }\rightarrow D^{\pm }\pi ^0\)  measured by BESIII Collaboration [10]} showed that
\(D^*_{s0}(2317)^-\)  tends to have a significantly
larger branching ratio to \(\pi ^0D^{*-}_s\)  than to \(\gamma D^{*-}_s\) , which differs from the expectation of the
conventional \(\bar{c}s\)  hypothesis. These puzzles inspired various exotic explanations to its inner structure,
such as \(DK\)  molecule state [11]}, [12]}, [13]}, [14]}, [15]}, a tetraquark state [16]}, [17]}, [18]}, [19]}, or a mixture of a
\(\bar{c} s\)  state and a tetraquark state [20]}, [21]}, [22]}. In order to further reveal the internal structure
of \(D^*_{s0}(2317)\) , we intend to study the weak production of this charmed-strange meson through the \(B_{(s)}\) 
decays, which can serve as an ideal platform to probe the valuable informations on the inner structure of
the exotic scalar mesons [23]}, [24]}, [25]}, [26]}, [27]}. In the conventional two quark picture the branching ratios of the
decays \(B_{(s)}\rightarrow D^*_{s0}(2317)P(V)\) , where \(P\)  (\(V\) ) denotes the light pseudoscalar
(vector) meson, are expected to be of the same order of magnitude as those of \(B_{(s)}\rightarrow D_{s}P(V)\)  decays, since the \(D^*_{s0}(2317)\)  meson
decay constant should be close to that of the pseudoscalar meson \(D_s\)  as required by the chiral symmetry. On the contrary, in the unconventional
picture the corresponding decay amplitudes involve additional hard scattering with the participation of four valence quarks. Then the branching ratios are at
least suppressed by the coupling constant and by inverse powers of heavy meson masses, such that they are much smaller than those of \(B_{(s)}\rightarrow D_{s}P(V)\)  decays
by one order. So it is meaningful to study the branching ratios of the decays \(B_{(s)}\rightarrow D^*_{s0}(2317)P(V)\)  both in experiment and theory.
